Non-vanishing of derivatives of -functions

Author:
Qingfeng Sun

Journal:
Proc. Amer. Math. Soc. **140** (2012), 449-463

MSC (2010):
Primary 11F67, 11F12, 11F30

Published electronically:
June 14, 2011

MathSciNet review:
2846314

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Abstract: Let be a fixed self-dual Hecke-Maass cusp form for and let be an orthogonal basis of holomorphic cusp forms of weight for . We prove an asymptotic formula for the first moment of the first derivative of at the central point , where runs over , , large enough. This implies that for each large enough there exists with such that .

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Additional Information

**Qingfeng Sun**

Affiliation:
School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, People’s Republic of China

Email:
qfsun@mail.sdu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-2011-10947-X

Keywords:
Non-vanishing,
$GL(3) ×GL(2)$ $L$-functions

Received by editor(s):
April 2, 2010

Received by editor(s) in revised form:
September 24, 2010, November 28, 2010, and November 29, 2010

Published electronically:
June 14, 2011

Additional Notes:
The author was supported by National Natural Science Foundation of China (grant No. 10971119).

Communicated by:
Kathrin Bringmann

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.